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Bunuel
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M08-07 13 Jun 2024, 00:08
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unicornilove
Confusing, there are 60 people who do not like either strawberry or apple jam. but if there are 80  peolpe who like R, where does the 20 shortfall go?
Bunuel
Official Solution:

Out of 200 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the maximum number of people who like raspberry jam but do not like either strawberry or apple jam?

A. 20
B. 60
C. 80
D. 86
E. 92


Consider the diagram below:



Notice that "30% of the people like both strawberry and apple jam" doesn't imply that none of these 30% (60 people) can also like raspberry jam. The intersection of the strawberry and apple jam groups is represented by the yellow segment in the diagram.

No specific formula is needed to solve this question: 112 people like strawberry jam, 88 people like apple jam, and 60 people like both strawberry and apple jam. Thus, the number of people who like either strawberry or apple jam (or both) is \(112 + 88 - 60 = 140\) (the area covered by Strawberry and Apple in the diagram). Therefore, there are a total of \(200 - 140 = 60\) people who "do not like either strawberry or apple jam." Can all of these 60 people like raspberry jam? Since there are 80 people who like raspberry jam (\(\text{Raspberry} = 80 \ge 60\)), it is possible! The maximum number of people who like raspberry jam and don't like either strawberry or apple jam is 60 (the gray segment in the diagram). In this case, the number of people who don't like any of the three jams (the area outside the three circles) would be zero.

Side note: The minimum number of people who like raspberry jam and don't like either strawberry or apple jam would be zero (if the Raspberry circle is entirely inside the Strawberry and/or Apple circles). In this case, the 60 people who "do not like either strawberry or apple jam" would be those who don't like any of the three jams.


Answer: B
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­These 20 people can like strawberry, apple or both.
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M08-07 20 Jul 2024, 04:06
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­Hi

From the statement in the question, doesn't it mean that only the intersection between strawberry and apple and not raspberry is 30%?

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M08-07 20 Jul 2024, 07:26
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gagan03
­Hi

From the statement in the question, doesn't it mean that only the intersection between strawberry and apple and not raspberry is 30%?

Regards

Gagan
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­No. "30% of the people like both strawberry and apple jam" doesn't imply that none of these 30% (60 people) can also like raspberry jam.
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M08-07 20 Oct 2024, 20:55
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I think this is a high-quality question and I agree with explanation.
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awaikar
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M08-07 23 Mar 2025, 17:49
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I like the solution - it’s helpful.
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